integral from 0 to 1 of (x+3sqrt(1-x^2))

Lösung

\int_{0}^{1} (x + 3 1 - x^{2}) d x

\frac{1}{2} + \frac{3 π}{4}

Dezimale

2.85619 \dots

Schritte zur Lösung

\int_{0}^{1} x + 3 1 - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x d x + \int_{0}^{1} 3 1 - x^{2} d x

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 3 1 - x^{2} d x = \frac{3 π}{4}

= \frac{1}{2} + \frac{3 π}{4}

\int_{1}^{2} \frac{8 - 3 x}{x ^{3}} d x

\int_{0}^{π} sin (2 x) + 4 sin (x) d x

\int_{0}^{4} \frac{1}{x ^{4} - 16} d x

\int_{0}^{1} x (x + 0.5) d x

\int_{- 1}^{u} \frac{1}{x + x ^{2}} d x